To extend the the use of spectral graph methods to the unsupervised representation and matching of articulated shapes, one can use local isometries as invariants preserved by articulated motion (except in the vicinities of the joint). Methods such as Laplacian Eigenmaps [1]}, generally used for dimensionality reduction, are explicitly conceived to find a mapping that best preserves such pairwise relationships.
Indeed, the Laplacian matrix [2]} encodes local geometric and topological properties of a graph, and hence it is well suited for describing articulated objects. Belkin and Niyogi [1]} provide a theoretical justification for combining the Laplacian operator with the Gaussian (or heat) kernel. Laplacian embedding has strong links with spectral clustering [4]} and with other local-based embedding methods such as LLE [5]}. In [6]}, the Laplacian embedding is used to embed 3-D meshes using a global geodesic distance and to match the embeddings using the ICP algorithm [7]}.
